Connive appears on creature cards and is a triggered ability. Whenever a creature connives, you draw a card and discard a card – and if the card you discarded was a nonland card, that creature gets a +1/+1 counter. Sometimes, connive will be written as connive X, where X will be some variable or number, like on Raffine. In that case, you draw X cards and discard X cards, but still only place one +1/+1 counter on the creature that connived.
So, conniving is essentially looting with a bit of possible upside stapled onto it. There’s not really a lot more to it – the only real note is that if a currently conniving creature is killed, bounced, exiled, or removed from the battlefield in any other way in response to the connive trigger, you still get to draw the card (or cards) and discard a card (or cards), but you’ll have a tricky time putting the +1/+1 counter on a creature that is no longer there. Also of note: connive is not a may, when you are instructed to connive, you do have to draw and discard appropriately.
These kinds of mechanics that can help you get through your deck – scry, surveil, especially cycling – are always very useful and well liked, as it turns out people like getting to play as much of their deck as they can. Connive looks ready to slot right into that same category, so don’t be surprised to see some cards with it making an impact.
If you want to start conniving, Magically-speaking, head over to cardkingdom.com!